algebra help

Let us call the three unknown angles in the triangle x, y and z. We can solve for each of these by setting up a system of equations and using the substitution method. Since one angle is three times as large as the smallest angle, our first equation will be 3x = y. Since the third angle is 45 degrees more than the smallest angle, our second equation will be x + 45 = z (notice that we designate x as being the smallest angle instead of y, because of our first equation). Finally, since the sum of all three angles in any triangle will always be 180 degrees, our third equation will be x + y + z = 180.

Let us substitute the values for y and z given in the first and second equations into the third equation. In this case, the third equation will read as follows:   x + 3x + (x + 45) = 180. Solving this equation yields x as being equal to 27. Now, plug x into the first equation (3x = y) to yield 81 for y. Finally, plug x into the second equation (x + 45 = z) to yield 72 for z. Since x = 27, y = 81, and z = 72, the largest angle is y, which measures 81 degrees. You can verify that the measures of x, y and z are correct by finding their sum, which is indeed 180 degrees.